ALBANY — Nearly half of SUNY students would fail the American history test given immigrants, a shocking new survey shows.

Forty-five percent of the 800 State University students surveyed last month could not correctly answer at least seven of 10 basic American history questions on the citizenship test, according to the survey released yesterday by John Zogby International.

To become citizens, immigrants must answer at least seven of the 10 questions correctly.

SUNY students fared even worse when asked 10 multiple-choice questions drawn from U.S. history Regents high-school exams and 10 other general American-history questions.

For instance, 93.6 percent of those surveyed knew Leonardo DiCaprio starred in the blockbuster movie “Titanic.” But 84 percent couldn’t name New York’s two U.S. senators: Daniel Patrick Moynihan and Charles Schumer.

The survey was commissioned by the Center for Excellence in Higher Education, an Albany-based conservative think tank that has released a series of critical reports on SUNY over the past five years.

“The center’s survey reveals a shocking lack of knowledge about American history among State University students,” said the center’s executive director, Tom Carroll.

Many SUNY students couldn’t list the order of major U.S. military initiatives of the 20th century or name America’s three World War II enemies.

Embarrassed SUNY officials said the survey findings “provide valuable insight” into the needs of high-school and college education in New York.

“We want our students to be better informed and more knowledgeable than the survey indicates,” SUNY spokesman Jon Sorenson said.

SUNY last year adopted a systemwide, 30-credit general-education requirement designed to ensure students take more classes like American history.